{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T02:48:44Z","timestamp":1769741324692,"version":"3.49.0"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2019,2,20]],"date-time":"2019-02-20T00:00:00Z","timestamp":1550620800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Mach Learn"],"published-print":{"date-parts":[[2019,5]]},"DOI":"10.1007\/s10994-019-05786-2","type":"journal-article","created":{"date-parts":[[2019,2,20]],"date-time":"2019-02-20T17:54:58Z","timestamp":1550685298000},"page":"809-830","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["N-ary decomposition for multi-class classification"],"prefix":"10.1007","volume":"108","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4675-7055","authenticated-orcid":false,"given":"Joey Tianyi","family":"Zhou","sequence":"first","affiliation":[]},{"given":"Ivor W.","family":"Tsang","sequence":"additional","affiliation":[]},{"given":"Shen-Shyang","family":"Ho","sequence":"additional","affiliation":[]},{"given":"Klaus-Robert","family":"M\u00fcller","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,2,20]]},"reference":[{"key":"5786_CR1","first-page":"113","volume":"1","author":"EL Allwein","year":"2001","unstructured":"Allwein, E. L., Schapire, R. E., & Singer, Y. (2001). Reducing multiclass to binary: A unifying approach for margin classifiers. Journal of Machine Learning Research, 1, 113\u2013141.","journal-title":"Journal of Machine Learning Research"},{"key":"5786_CR2","unstructured":"Bengio, S., Weston, J., & Grangier, D. (2010). Label embedding trees for large multi-class tasks. In NIPS (pp. 163\u2013171)."},{"key":"5786_CR3","unstructured":"Beygelzimer, A., Langford, J., Lifshits, Y., Sorkin, G., & Strehl, A. (2009). Conditional probability tree estimation analysis and algorithms. In UAI (pp. 51\u201358)."},{"key":"5786_CR4","series-title":"Statistics\/probability series","volume-title":"Classification and regression trees","author":"L Breiman","year":"1984","unstructured":"Breiman, L., Friedman, J. H., Olshen, R. A., & Stone, C. J. (1984). Classification and regression trees., Statistics\/probability series Belmont, California: Wadsworth Publishing Company."},{"issue":"3","key":"5786_CR5","doi-asserted-by":"publisher","first-page":"27:1","DOI":"10.1145\/1961189.1961199","volume":"2","author":"C-C Chang","year":"2011","unstructured":"Chang, C.-C., & Lin, C.-J. (2011). Libsvm: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology, 2(3), 27:1\u201327:27.","journal-title":"ACM Transactions on Intelligent Systems and Technology"},{"issue":"1","key":"5786_CR6","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1109\/TIT.1967.1053964","volume":"13","author":"T Cover","year":"1967","unstructured":"Cover, T., & Hart, P. (1967). Nearest neighbor pattern classification. IEEE Transactions on Information Theory, 13(1), 21\u201327.","journal-title":"IEEE Transactions on Information Theory"},{"key":"5786_CR7","first-page":"265","volume":"2","author":"K Crammer","year":"2002","unstructured":"Crammer, K., & Singer, Y. (2002). On the algorithmic implementation of multiclass kernel-based vector machines. Journal of Machine Learning Research, 2, 265\u2013292.","journal-title":"Journal of Machine Learning Research"},{"key":"5786_CR8","unstructured":"Deng, J., Satheesh, S., Berg, A., & Fei-Fei, L. (2011). Fast and balanced: Efficient label tree learning for large scale object recognition. In NIPS."},{"key":"5786_CR9","doi-asserted-by":"crossref","unstructured":"Dietterich, T. G. (2000). Ensemble methods in machine learning. In MCS (pp. 1\u201315). Springer.","DOI":"10.1007\/3-540-45014-9_1"},{"key":"5786_CR10","unstructured":"Dietterich, T. G., & Bakiri, G. (1991). Error-correcting output codes: A general method for improving multiclass inductive learning programs. In AAAI (pp. 572\u2013577). AAAI Press."},{"key":"5786_CR11","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1613\/jair.105","volume":"2","author":"TG Dietterich","year":"1995","unstructured":"Dietterich, T. G., & Bakiri, G. (1995). Solving multiclass learning problems via error-correcting output codes. Journal of Artificial Intelligence Research, 2, 263\u2013286.","journal-title":"Journal of Artificial Intelligence Research"},{"issue":"3","key":"5786_CR12","doi-asserted-by":"publisher","first-page":"696","DOI":"10.1109\/TNN.2006.872343","volume":"17","author":"B Fei","year":"2006","unstructured":"Fei, B., & Liu, J. (2006). Binary tree of SVM: A new fast multiclass training and classification algorithm. IEEE Transactions on Neural Networks, 17(3), 696\u2013704.","journal-title":"IEEE Transactions on Neural Networks"},{"issue":"8","key":"5786_CR13","doi-asserted-by":"publisher","first-page":"1761","DOI":"10.1016\/j.patcog.2011.01.017","volume":"44","author":"M Galar","year":"2011","unstructured":"Galar, M., Fern\u00e1ndez, A., Barrenechea, E., Bustince, H., & Herrera, F. (2011). An overview of ensemble methods for binary classifiers in multi-class problems: Experimental study on one-vs-one and one-vs-all schemes. Pattern Recognition, 44(8), 1761\u20131776.","journal-title":"Pattern Recognition"},{"key":"5786_CR14","unstructured":"Gao, T., & Koller, D. (2011). Discriminative learning of relaxed hierarchy for large-scale visual recognition. In ICCV (pp. 2072\u20132079)."},{"issue":"2","key":"5786_CR15","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1016\/j.inffus.2010.06.010","volume":"12","author":"N Garc\u00eda-Pedrajas","year":"2011","unstructured":"Garc\u00eda-Pedrajas, N., & Ortiz-Boyer, D. (2011). An empirical study of binary classifier fusion methods for multiclass classification. Information Fusion, 12(2), 111\u2013130.","journal-title":"Information Fusion"},{"issue":"2","key":"5786_CR16","doi-asserted-by":"publisher","first-page":"662","DOI":"10.1016\/j.patcog.2007.07.004","volume":"41","author":"J-H Hong","year":"2008","unstructured":"Hong, J.-H., Min, J.-K., Cho, U.-K., & Cho, S.-B. (2008). Fingerprint classification using one-vs-all support vector machines dynamically ordered with Na\u00efve Bayes classifiers. Pattern Recognition, 41(2), 662\u2013671.","journal-title":"Pattern Recognition"},{"issue":"10","key":"5786_CR17","doi-asserted-by":"publisher","first-page":"e42947","DOI":"10.1371\/journal.pone.0042947","volume":"7","author":"R Jenssen","year":"2012","unstructured":"Jenssen, R., Kloft, M., Zien, A., Sonnenburg, S., & M\u00fcller, K.-R. (2012). A scatter-based prototype framework and multi-class extension of support vector machines. PLoS ONE, 7(10), e42947.","journal-title":"PLoS ONE"},{"issue":"13\u201314","key":"5786_CR18","doi-asserted-by":"publisher","first-page":"1163","DOI":"10.1016\/j.imavis.2003.09.013","volume":"21","author":"J Kittler","year":"2003","unstructured":"Kittler, J., Ghaderi, R., Windeatt, T., & Matas, J. (2003). Face verification via error correcting output codes. Image and Vision Computing, 21(13\u201314), 1163\u20131169.","journal-title":"Image and Vision Computing"},{"key":"5786_CR19","unstructured":"Knerr, S., Personnaz, L., & Dreyfus, G. (1990). Single-layer learning revisited: A stepwise procedure for building and training a neural network. In F. F. Souli\u00e9 & J. H\u00e9rault (Eds.), Neurocomputing. NATO ASI Series (Series F: Computer and Systems Sciences), Vol. 68. Berlin, Heidelberg: Springer."},{"key":"5786_CR20","first-page":"2269","volume":"12","author":"F Lauer","year":"2011","unstructured":"Lauer, F., & Guermeur, Y. (2011). MSVMpack: A multi-class support vector machine package. Journal of Machine Learning Research, 12, 2269\u20132272.","journal-title":"Journal of Machine Learning Research"},{"key":"5786_CR21","doi-asserted-by":"crossref","unstructured":"Liu, X.-Y., Li, Q.-Q., & Zhou, Z.-H. (2013). Learning imbalanced multi-class data with optimal dichotomy weights. In IEEE 13th international conference on data mining (ICDM) (pp. 478\u2013487). IEEE.","DOI":"10.1109\/ICDM.2013.51"},{"issue":"1","key":"5786_CR22","first-page":"81","volume":"1","author":"JR Quinlan","year":"1986","unstructured":"Quinlan, J. R. (1986). Induction of decision trees. Machine Learning, 1(1), 81\u2013106.","journal-title":"Machine Learning"},{"issue":"2","key":"5786_CR23","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1109\/TNNLS.2013.2274735","volume":"25","author":"A Rocha","year":"2014","unstructured":"Rocha, A., & Goldenstein, S. (2014). Multiclass from binary: Expanding one-vs-all, one-vs-one and ECOC-based approaches. IEEE Transactions on Neural Networks and Learning Systems, 25(2), 289\u2013302.","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"key":"5786_CR24","unstructured":"Su, J., & Zhang, H. (2006). A fast decision tree learning algorithm. In Proceedings of the 21st national conference on artificial intelligence, AAAI\u201906 (Vol. 1, pp. 500\u2013505). AAAI Press."},{"key":"5786_CR25","first-page":"363","volume":"6","author":"IW Tsang","year":"2005","unstructured":"Tsang, I. W., Kwok, J. T., & Cheung, P. (2005). Core vector machines: Fast SVM training on very large data sets. Journal of Machine Learning Research, 6, 363\u2013392.","journal-title":"Journal of Machine Learning Research"},{"issue":"3","key":"5786_CR26","doi-asserted-by":"publisher","first-page":"675","DOI":"10.1016\/j.dsp.2006.11.009","volume":"17","author":"ED \u00dcbeyli","year":"2007","unstructured":"\u00dcbeyli, E. D. (2007). Ecg beats classification using multiclass support vector machines with error correcting output codes. Digital Signal Processing, 17(3), 675\u2013684.","journal-title":"Digital Signal Processing"},{"issue":"Aug","key":"5786_CR27","first-page":"975","volume":"5","author":"T-F Wu","year":"2004","unstructured":"Wu, T.-F., Lin, C.-J., & Weng, R. C. (2004). Probability estimates for multi-class classification by pairwise coupling. Journal of Machine Learning Research, 5(Aug), 975\u20131005.","journal-title":"Journal of Machine Learning Research"},{"key":"5786_CR28","unstructured":"Yang, J.-B., & Tsang, I. W. (2011). Hierarchical maximum margin learning for multi-class classification. In UAI."},{"key":"5786_CR29","unstructured":"Yu, Z., Cai, D., & He, X. (2010). Error-correcting output hashing in fast similarity search. In Proceedings of the second international conference on internet multimedia computing and service, ICIMCS \u201910 (pp. 7\u201310). New York, NY, USA: ACM."},{"key":"5786_CR30","doi-asserted-by":"crossref","unstructured":"Zhao, B., & Xing, E. P. (2013). Sparse output coding for large-scale visual recognition. In CVPR (pp. 3350\u20133357). IEEE.","DOI":"10.1109\/CVPR.2013.430"},{"key":"5786_CR31","unstructured":"Zhong, G., & Cheriet, M. (2013). Adaptive error-correcting output codes. In IJCAI (pp. 1932\u20131938)."},{"issue":"4","key":"5786_CR32","doi-asserted-by":"publisher","first-page":"1091","DOI":"10.1016\/j.patcog.2012.10.015","volume":"46","author":"G Zhong","year":"2013","unstructured":"Zhong, G., & Liu, C.-L. (2013). Error-correcting output codes based ensemble feature extraction. Pattern Recognition, 46(4), 1091\u20131100.","journal-title":"Pattern Recognition"}],"container-title":["Machine Learning"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10994-019-05786-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-019-05786-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-019-05786-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,2,19]],"date-time":"2020-02-19T20:02:49Z","timestamp":1582142569000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10994-019-05786-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,20]]},"references-count":32,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2019,5]]}},"alternative-id":["5786"],"URL":"https:\/\/doi.org\/10.1007\/s10994-019-05786-2","relation":{},"ISSN":["0885-6125","1573-0565"],"issn-type":[{"value":"0885-6125","type":"print"},{"value":"1573-0565","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2,20]]},"assertion":[{"value":"27 February 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 January 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 February 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}